Bit-Reversible Version of Milne’s Fourth-Order Time-Reversible Integrator for Molecular Dynamics

• Autorzy: Hoover W. G. , Hoover C. G.

Identyfikatory

DOI

10.12921/cmst.2017.0000031

• Języki publikacji: EN

Abstrakty

EN

We point out that two of Milne’s fourth-order integrators are well-suited to bit-reversible simulations. The fourth-order method improves on the accuracy of Levesque and Verlet’s algorithm and simplifies the definition of the velocity v and energy e = (q2 + v2)=2. (We use this one-dimensional oscillator problem as an illustration throughout this paper). Milne’s integrator is particularly useful for the analysis of Lyapunov (exponential) instability in dynamical systems, including manybody molecular dynamics. We include the details necessary to the implementation of Milne’s Algorithms.

Słowa kluczowe

EN

bit-reversible molecular dynamics; Lyapunov instability; chaotic dynamical systems

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2017
• Tom: Vol. 23, No. 4
• Strony: 299--303
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Hoover W. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA

autor

Hoover C. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA

Bibliografia

• [1] W. E. Milne, Numerical Calculus – Approximations, Interpolation, Finite Differences, Numerical Integration, and Curve Fitting (Princeton University Press, 1949 and 2015).
• [2] D. Levesque and L. Verlet, Molecular Dynamics and Time Reversibility, Journal of Statistical Physics 72, 519-537 (1993).
• [3] L. Verlet, ‘Computer Experiments’ on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review 159, 98-103 (1967).
• [4] H. A. Posch and W. G. Hoover, Large-System Phase-Space Dimensionality Loss in Stationary Heat Flows, Physica D 187, 281-293 (2004).
• [5] O. Kum and Wm. G. Hoover, Time-Reversible Continuum Mechanics, Journal of Statistical Physics 76, 1075-1081 (1994).
• [6] B. L. Holian, Wm. G. Hoover, and H. A. Posch, Resolution of Loschmidt’s Paradox: The Origin of Irreversible Behavior in Reversible Atomistic Dynamics, Physical Review Letters 59, 10-13 (1987).
• [7] C. Grebogi, E. Ott, and J. A. Yorke, Roundoff-Induced Periodicity and the Correlation Dimension of Chaotic Attractors, Physical Review A 38, 3688-3692 (1988).
• [8] C. Dellago and Wm. G. Hoover, Finite-Precision Stationary States At and Away from Equilibrium, Physical Review E 62, 6275-6281 (2000).
• [9] M. Romero-Bastida, D. Pazó, J. M. Lopéz, and M. A. Rodriguez, Structure of Characteristic Lyapunov Vectors in Anharmonic Hamiltonian Lattices, Physical Review E 82, 036205 (2010).
• [10] Wm. G. Hoover and Carol G. Hoover, Time-Symmetry Breaking in Hamiltonian Mechanics, Computational Methods in Science and Technology 19, 77-87 (2013).
• [11] Wm. G. Hoover and C. G. Hoover, The Kharagpur Lectures (World Scientific, Singapore, 2018, in preparation).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).